Since long ago you can connect to websites using metamask or some other EVM wallets.
But recently I noticed that you can now connect using your bitcoin wallets as well. Some wallets allows this. Accorgin to unisat.io, these wallets allows bitcoin connect:
UniSat Wallet
Xverse Wallet
Leather Wallet
OKX Wallet
Bitget Wallet
Phantom Wallet
Magic Eden
Enkrypt
I just use Phantom, and used UniSat a few times. Have you tried them?
I think the question should be, or the question I have is, are there any smart contract on the bitcoin network to interact with when you connect any of those mentioned wallet to any website? And I think the answer (obviously) is no, so I essence, it's good if we understand that when you connect any of the mentioned wallet to any WEB3 site, you are not connected to a bitcoin network, but you are connected to the network (EVM and NON - EVM(example - Solana) that that WEB3 site supports.
There are no smart contracts running on the bitcoin network, so of what use is it connecting a bitcoin wallet to a web3 platform, when you can't make payments, or buy/sell original bitcoin in a decentralized and automatic way or form using smart contracts?